Due to the recent interest in magnetic light-matter interactions, the magnetic dipole (MD) transitions in lanthanide ions have been studied for potential applications in nano-optics. Similar to lanthanide ions, transition-metal ions also exhibit strong MD emission at room temperature, but their prominent MD zero-phonon lines are often accompanied by significant electric dipole (ED) sideband emission. Here, we extend energy-momentum spectroscopy to time-resolved measurements, and use this technique to quantify the ED and MD contributions to light emission from trivalent chromium doped magnesium oxide (Cr(3+):MgO). This allows us to differentiate the MD (2)E → (4)A2 zero-phonon line from phonon-assisted (2)E → (4)A2 and (4)T2 → (4)A2 ED sidebands. We also demonstrate how the relative intensities of the sharp MD zero-phonon line and the broad ED sidebands can be used as a qualitative measure of the MD and ED local density of optical states.
The Raman relaxation rates for
Ni2+ and
Cr3+ ions in MgO crystals have been calculated using a shell model of phonons which is in good agreement with the results of neutron scattering experiments. These shell-model results are compared with those obtained with the Debye model for the phonons and, also, with the available experimental results for
Ni2+ and
Cr3+ in MgO. In the case
Ni2+, 50\ifmmode^\circ\else\textdegree\fi{}K is the highest temperature for which the relaxation time is sufficiently long to be directly measureable. As might be expected, in this low-temperature region the results based on the shell model and the Debye model of phonons are not significantly different. However, the values of relaxation rates at 123 and 136\ifmmode^\circ\else\textdegree\fi{}K obtainable from the recent line-shape measurements for
Ni2+ in MgO are in good agreement with those calculated on the basis of the shell model of phonons. In the case of
Cr3+ ions, the relaxation time can be measured directly up to temperatures as high as 200\ifmmode^\circ\else\textdegree\fi{}K, and in this range of temperature the two sets of results differ considerably. With the shell model, we obtain good agreement with the experimental results on the functional dependence of the relaxation rate
T11 on temperature. However, the absolute values of
T11 for
Cr3+ obtained with this phonon model are on the average less than the experimental measurements by a factor of 5. The possible sources which might be important in bridging the gap between the theoretical and experimental results are discussed.
The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94%
Cr3+ were studied from 13 to 700\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion (
R) lines and the pair (
N) lines are proportional to Boltzmann factors ${e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$, where $\ensuremath{\Delta}E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the
R and
N lines are pure exponentials in the temperature region where the
N lines follow a Boltzmann law; at low temperatures the
N lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.
The linewidths and line positions of 4I15/2 to 4I13/2 absorption transitions of trivalent erbium in CsCdBr₃ and CaF₂ were measured as a function of temperature from approximately 10 K to 300 K. By comparing the temperature dependence of these transitions with theoretical models of electron-phonon coupling the primary mechanism involved were determined. For Er3+ doped CaF₂ the Raman scattering processes dominated the line broadening, although the single-phonon direct processes were significant enough to drastically alter the values of the Raman scattering electron-phonon coupling constant. In comparison, the Er³⁺ doped CsCdBr₃ had negligible Raman scattering contributing to the line broadening. This is likely due to the exceedingly low Debye temperature and consequently low number of phonons, reducing the likelihood of two-phonon processes relative to single-phonon processes. The results were then analysed in terms of the bond length with the ligands and compared with other studies showing that as the bond length gets shorter the electron-phonon coupling constant associated with Raman scattering is expected to get smaller. To explain the line shifts in CaF₂:Er³⁺ it is necessary to treat the Debye temperature as a parameter. This indicates that the phonon modes causing the line shifts are different from those causing the line broadening, and in most of the cases are vibronic processes rather than Raman processes. In the case of CsCdBr₃:Er³⁺ there is very little difference between the fits using the fixed Debye temperature and a varied Debye temperature in over half of the cases examined. Given the distribution of phonon modes, it is likely that this small difference arises because combinations of these processes are of similar intensity, meaning that a combination of Raman and optical phonon modes are likely causing the line shift.
The optical energy transfer between Cr 3+ ions from cubic centres to tetragonal centres is measured. Transfer is observed only when the donor is very close to the acceptor and the measured transfer times are relatively short ( approximately 100 mu s). The tetragonal acceptors are Cr 3+ -ion pairs which form different triads with the donor. It is deduced that transfer to rhombic sites is also rapid only from very close cubic centres. The shortness of the transfer times explains why a spin memory is observed during the energy transfer from cubic to rhombic centres. The localisation of optical excitation in triads is due to the presence of charge-compensating Mg 2+ vacancies and the inefficiency of the dipole-dipole interaction.
When the coupling between two ions associated in pair exceeds a given value, the excitation of both ions of the pair is impossible when using a single narrow laser. This double excitation was obtained with two lasers of different wavelengths. A narrowing of the inhomogeneous broadened lines is observed which gives information on the strain field in the crystal. From the difference between the wavelengths, the order of magnitude of the coupling is deduced and compared with phonon assisted transfer rates.